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What is a Derivative?

Types of Problems:

• Defining Average and Instantaneous Rates of Change at a Point
• Defining a Derivative of a Function and using Derivative Notation
  
• Estimating Derivatives of a Function at a Point
  

Notes & Handouts

Practice 

Video and other resources

Digital Resources

Desmos Files
(these files investigate the following)

• Instantaneous rate of change at a given point
• Slope of tangent line for a function at a given point
• Linear function y = x
• Quadratic Function y=x^2
• ​Cubic Function y=x^3
• Square Root Function
• ​Cube Root Function
• Rational Function y =1/x

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Connecting Differentiability and Continuity

Types of Problems:

• What does it mean to be differentiable?
• What does it mean to be continuous?
• Determining when derivatives do and do not exist

Notes & Handouts

Practice

​Video and other resources

​Digital Resources

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Power Rule for Derivatives

​Types of Problems:

• Using Power Rule to determine the derivative at a point
• Proving the Power Rule with the use of limits and limit properties

​Practice

​Video and other resources

​Notes & Handouts

​​Digital Resources

Desmos Files
(these files investigate the following)

• Instantaneous rate of change at a given point
• Slope of tangent line for a function at a given point
• Linear Functions (slope intercept form)
• Quadratic Function in standard form 
• ​Cubic Function in standard form​

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Basic Rules for Differentiation

​Types of Problems:

• Using Constant Rule to determine the derivative at a point
• Proving the Constant Rule with the use of limits and limit properties
• Using Sum or Difference Rule to determine the derivative at a point
• Proving the Sum and Difference Rules with the use of limits and limit properties
• Using Constant Multiple Rule to determine the derivative at a point
• Proving the Constant Multiple Rule with the use of limits and limit properties

​Practice

​Video and other resources

​Notes & Handouts

​Digital Resources

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Derivatives of cos x, sin x, b^x, e^x, log b x, and ln x

​​Types of Problems:

• Using Cosine Derivative Rule to determine the derivative at a point
• Using Sine Derivative Rule to determine the derivative at a point
• Using Derivative of e^x Rule to determine the derivative at a point
• Using Derivative of ln x Rule to determine the derivative at a point

​​Notes & Handouts

​​Practice

​Video and other resources

​Digital Resources

​Desmos Files
(these files investigate the following)

• Instantaneous rate of change at a given point
• Slope of tangent line for a function at a given point

• Exponential Functions base b 
• Exponential Functions base e
• Logarithmic Functions base b
  
• Logarithmic Functions base e

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Product and Quotient Rule

​​Types of Problems:

• Using Product Rule to determine the derivative at a point
• Using Quotient Rule to determine the derivative at a point
• Using Negative Exponents to use Product Rule instead of Quotient Rule

​​Practice

​Video and other resources

​​Notes & Handouts

​Digital Resources

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Derivatives of tan x, cot x,  sec x, and csc x

​​​Types of Problems:

• Using Tangent Derivative Rule to determine the derivative at a point
• Using Cotangent Derivative Rule to determine the derivative at a point
• Using Secant Derivative Rule Rule to determine the derivative at a point
• Using Cosecant Derivative Rule to determine the derivative at a point

​​​Notes & Handouts

​​​Practice

​​Video and other resources

​​Digital Resources

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Additional Resources

Professor Leonard's You Tube Channel ​

Paul's Online Notes for Calc 1

Overview of Topics

KHAN Academy: Derivatives

​​CK 12 Link: Derivatives

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